In my class, I have a quote of the day; today I had a double feature. A matched set, if you like.
A man should be learned in several sciences, and should have . . . , in some measure, a mathematical mind, to be a complete poet. —Dryden
A mathematician who is not also something of a poet will never be a complete mathematician. —Weierstraß
Isn’t that remarkable? Most people probably think of poetry and mathematics as somehow polar opposites, or at the very least unrelated. But then, it is a sad reflection of the way math is taught in this society, most people have no clear sense of what mathematics is or why we do it. What can we take from the fact that so many great mathematicians see a connection, and at least some of the great poets see it too (maybe “many” would be apt here too, but I am not an expert in poets). I love the sentiment expressed above, that somehow the two are necessary to complete each other. Rings true for me.
Indeed, mathematics and poetry are sisters. The goal of both is to interact with ideas in their most elemental form. To the extent there is a difference it is in the interpretation of the phrase “in their most elemental form”.
When I said this during today’s lecture in my class, which is a geometry class for future teachers, two of my students (much to their credit) asked me “Dr. Cap, what can we do as teachers to bring this to our students?”
*sigh* Boy, if ever there were a question that I wanted the answer to…
The short answer: follow the beauty. I often say that I’m a mathematician for purely aesthetic reasons. Feel the beauty of the mathematical ideas, and let that be the motivator of pedagogy.
I’m not negating the practical value of mathematics for real life, nor the important of students’ learning how to actually get correct answers to math questions; I just believe that following the poetry of the ideas will lead you all the places you need to go.
You know who I think are good role models in this general direction? The people behind RadioLab. If you have ears and you’ve never heard any of these absolute gems of radio, go listen to one right now. Any one. Their focus is more on scientific ideas and how they interface with philosophy and the human experience (though they verge into mathematics sometimes, such as in the “Emergence” production), but I mean it. Go there right now. I’d love to see more done along these lines for mathematical ideas.
(When I went to retrieve this link, I found their most recent episode is called “Numbers”, and I haven’t heard it yet. I’m excited. Apparently my exhortation to “listen to one right now” also applies to myself.)
Let me also plug The Heart of Mathematics, by Edward Burger and Michael Starbird. This textbook “gets it”, and if anything I have ever said in this blog rings true for you, and if you are any kind of a math educator of have plans to be one, then you should consider this required reading.